Question: $ E = \left[\begin{array}{rr}1 & -1 \\ -2 & 1\end{array}\right]$ $ F = \left[\begin{array}{rr}0 & -1 \\ -1 & -1\end{array}\right]$ Is $ E+ F$ defined?
In order for addition of two matrices to be defined, the matrices must have the same dimensions. If $ E$ is of dimension $( m \times  n)$ and $ F$ is of dimension $( p \times  q)$ , then for their sum to be defined: 1. $ m$ (number of rows in $ E$ ) must equal $ p$ (number of rows in $ F$ ) and 2. $ n$ (number of columns in $ E$ ) must equal $ q$ (number of columns in $ F$ Do $ E$ and $ F$ have the same number of rows? Yes Yes No Yes Do $ E$ and $ F$ have the same number of columns? Yes Yes No Yes Since $ E$ has the same dimensions $(2\times2)$ as $ F$ $(2\times2)$, $ E+ F$ is defined.